於圖形顯示卡上應用晶格波茲曼法 及局部加密網格計算流場

Simulation of fluid flow with Lattice Boltzmann method and local grid refinement on GPU

汪廷曜(Wang, Ting Yao)

指導教授 ： 林昭安

國立清華大學/工學院/動力機械工程學系/碩士(2016年)

摘要

對於晶格波茲曼法在模擬高雷諾數時，均勻網格無法精確的解析出渦流以及局部流場會出現非自然現象的震盪。因此，在物理變化劇烈的區域採用比較密的網格能有效解決上述的問題。在本論文，是在圖形顯示卡上應用晶格波茲曼法計算整個非均勻網格。雖然前後有許多學者已經提出以單鬆弛及多鬆弛的方式加密局部網格。然而，本論文利用二維以及三維拉板驅動空穴來驗證單鬆弛及多鬆弛的方式局部加密方法以及空間差分方法，並將三維方面的問題推廣到一維切割平行運算。在結果部分，本文探討了在不同雷諾數下粗網格以及細網格的交界面都能符合質、動量守恆。並且驗證了局部加密網格確實能改善局部渦旋的位置和震盪的現象。

關鍵字

晶格波茲曼法 ； 加密局部網格 ； 三維拉板驅動空穴 ； 圖形顯示卡

並列摘要

In its original form, lattice Boltzmann method is based on regular lattices. However, in order to enhance resolution at high Reynolds number or capture vortices accurately, regular grid may not be sufficient. One of the approaches to overcome this problem is to adopt local grid refinement. In this thesis, local grid refinement using lattice Boltzmann method on GPU is developed. Single relaxation time and multi-relaxation time LBM model with locally refined grid are adopted to compute two dimensional lid driven cavity flow. For three dimensional cavity flow, simulation are computed on multi-GPU with single relaxation model. Besides, a local cubic spatial interpolation which satisfies the mass and momentum continuity is used. Several cases are tested to investigate the method of grid refined scheme, interface structure and spatial interpolation between coarse and fined grids. The present strategy can greatly improve the accuracy of vortices and the impact of oscillation which is from singularity for viscous flow.

並列關鍵字

lattice Boltzmann method ； GPU ； local grid refinement ； lid driven cavity

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